A new approach to low-distortion embeddings of finite metric spaces into non-superreflexive Banach spaces

The main goal of this paper is to develop a new embedding method which we use to show that some finite metric spaces admit low-distortion embeddings into all non-superreflexive spaces. This method is based on the theory of equal-signs-additive sequences developed by Brunel and Sucheston (1975-1976). We also show that some of the low-distortion embeddability results obtained using this method cannot be obtained using the method based on the factorization between the summing basis and the unit vector basis of ℓ1, which was used by Bourgain (1986) and Johnson and Schechtman (2009).